Computes the bounded BunchKaufman factorization of a complex Hermitian matrix.
Syntax

lapack_int LAPACKE_chetrf_rook (int matrix_layout, char uplo, lapack_int n, lapack_complex_float * a, lapack_int lda, lapack_int * ipiv);
lapack_int LAPACKE_zhetrf_rook (int matrix_layout, char uplo, lapack_int n, lapack_complex_double * a, lapack_int lda, lapack_int * ipiv);
Include Files
 mkl.h
Description
The routine computes the factorization of a complex Hermitian matrix A using the bounded BunchKaufman diagonal pivoting method:

if uplo='U', A = U*D*U^{H}

if uplo='L', A = L*D*L^{H},
where A is the input matrix, U (or L ) is a product of permutation and unit upper ( or lower) triangular matrices, and D is a Hermitian blockdiagonal matrix with 1by1 and 2by2 diagonal blocks.
This is the blocked version of the algorithm, calling Level 3 BLAS.
Input Parameters
matrix_layout 
Specifies whether matrix storage layout for array b is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR). 
uplo 
Must be 'U' or 'L'. Indicates whether the upper or lower triangular part of A is stored: If uplo = 'U', the array a stores the upper triangular part of the matrix A. If uplo = 'L', the array a stores the lower triangular part of the matrix A. 
n 
The order of matrix A; n≥ 0. 
a 
Array a, size (lda*n) The array a contains the upper or the lower triangular part of the matrix A (see uplo). If uplo = 'U', the leading nbyn upper triangular part of a contains the upper triangular part of the matrix A, and the strictly lower triangular part of a is not referenced. If uplo = 'L', the leading nbyn lower triangular part of a contains the lower triangular part of the matrix A, and the strictly upper triangular part of a is not referenced. 
lda 
The leading dimension of a; at least max(1, n). 
Output Parameters
a 
The block diagonal matrix D and the multipliers used to obtain the factor U or L (see Application Notes for further details). 
ipiv 

Return Values
This function returns a value info.
If info = 0, the execution is successful.
If info = i, the ith parameter had an illegal value.
If info = i, D_{ii} is exactly 0. The factorization has been completed, but the block diagonal matrix D is exactly singular, and division by 0 will occur if you use D for solving a system of linear equations.
Application Notes
If uplo = 'U', thenA = U*D*U^{H}, where
U = P(n)*U(n)* ... *P(k)U(k)* ...,
i.e., U is a product of terms P(k)*U(k), where k decreases from n to 1 in steps of 1 or 2, and D is a block diagonal matrix with 1by1 and 2by2 diagonal blocks D(k). P(k) is a permutation matrix as defined by ipiv(k), and U(k) is a unit upper triangular matrix, such that if the diagonal block D(k) is of order s (s = 1 or 2), then
If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k1,k).
If s = 2, the upper triangle of D(k) overwrites A(k1,k1), A(k1,k), and A(k,k), and v overwrites A(1:k2,k1:k).
If uplo = 'L', then A = L*D*L^{H}, where
L = P(1)*L(1)* ... *P(k)*L(k)* ...,
i.e., L is a product of terms P(k)*L(k), where k increases from 1 to n in steps of 1 or 2, and D is a block diagonal matrix with 1by1 and 2by2 diagonal blocks D(k). P(k) is a permutation matrix as defined by ipiv(k), and L(k) is a unit lower triangular matrix, such that if the diagonal block D(k) is of order s (s = 1 or 2), then
If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).